Applications of...

A spherical balloon is filled with 4500π cu m of helium gas. If a leak in the balloon causes the gas to escape at the rate of 72 π cu m/min, then the rate (in m/min) at which the radius of the balloon decreases 49 min after the leakage began is

If y = 2x³ - 2x² + 3x -5, then for x = 2 and ∆x = 0.1, value of ∆y is

The distance (in metres) travelled by a vehicle in time t (in seconds) is given by the equation s = 3t³ + 2t² + t +1. The difference in the acceleration between t = 2 and t = 4 is

The equation of motion of a particle moving along a straight line is s = 2t³ - 9t² + 12 t, where the units of s and t are cm and s. The acceleration of the particle will be zero after

A particle is moving in a straight line. At time t, the distance between the particle from its starting point is given by x = t - 6t² + t³. Its acceleration will be zero at

The distance covered by a particle in t sec is given by x = 3 + 8t - 4t²

If a particle moves such that the displacement is proportional to the square of the velocity acquired, then its acceleration is

Let f : [0,1] → R(the set of all real numbers) be a function. Suppose the function f is twice differentiable,
f(0) = f(1) = 0 and satisfies f \'\'(x) - 2f \'(x) + f(x) ≥ e^x, x ϵ [0,1].
Which of the following is correct for 0 < x < 1?

The function f(x) = tan^-1 (sin x + cos x) is an increasing function in